Numbers Everywhere!

<LI>Find two different whole numbers such that neither number contains any zeros and their product yields 1000000000.
<LI>Four different whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the four original numbers that sum to 125?

Re: Numbers Everywhere!

Now you do have me stumped.

"Four different whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the four original numbers that sum to 125?"

1st number : 3
2nd number: 7
3rd number: 23
4th number: 92

3+7+23+92=125

1st number increased by 4: 7
2nd number decreased by 4: 3
3rd number multiplied by 4: 92
4th number divided by 4: 23

Same numbers as before, only in different order. Still add to 125.

Actually, there are more solutions: 8,12,21,84; 13,17,19,76; 18,22,17,68. I guess I don't understand the question.

Re: Solution

The numbers in yours (since you created the algebraic solution not based on the "order") is in the wrong order:
"Four different whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the four original numbers that sum to 125"

Now, when the first is increased by 4, the second is decreased by 4, the third is multiplied by 4 and the fourth is divided by 4 all give you <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">20</span hide>. In your order this does not work out... <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

Re: Solution

Solution

Perhaps the wording of the puzzle is a bit confusing. I apologize. The one and only correct solution along with the math behind it is noted below...

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The objective is to find four numbers that add to 125 whereby those four numbers become equivalent (the same number) after adding 4 to one, subtracting 4 from another, multiplying one by 4 and dividing the last by 4. If this is more clear than the original instructions, stop here before proceeding to the final solution...</span hide>

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">In the end, you have: 16 + 24 + 5 + 80 = 125. You can see now, that by adding 4 to one of the numbers, subtracting 4 from another of the numbers..., they all become equivalent (equal to 20).</span hide>